Abstract
In this thesis, we investigate dilaton quantum gravity using a functional renormalization group approach. We derive and discuss flow equations both in the background field approximation and using a vertex expansion as well as solve the fixed point equations globally to show how realistic gravity, connecting ultraviolet and infrared physics, can be realized on a pure fixed point trajectory by virtue of spontaneous breaking of scale invariance. The emerging physical system features a dynamically generated moving Planck scale resembling the Newton coupling as well as slow roll inflation with an exponentially decreasing effective cosmological constant that vanishes completely in the infrared. The moving Planck scale might make quantum gravity experimentally accessible at a different energy scale than previously believed. We therefore not only provide further evidence for the existence of a consistent quantum theory of gravity based on general relativity, but also offer potential solutions towards the hierarchy and cosmological constant problems, thereby opening up exciting opportunities for further research.
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